量子相变和分岔：量子晶格多体系统的约化保真度作为相变指标
Quantum phase transitions and bifurcations: reduced fidelity as a phase transition indicator for quantum lattice many-body systems
摘要：
我们建立了一个有趣的联系之间的量子相变和分叉的约化保真度之间的两个不同的约化密度矩阵的量子晶格多体系统的破缺订单。我们的发现是基于这样的观察，在传统的Landau-Ginzburg-Wilson范式中，一个量子系统经历相变的特征在于自发对称性破缺，它被局部序参量捕获，这反过来又导致了在对称性破缺相中约化的密度矩阵的本质变化。在一维空间中无限晶格上的两个量子系统，即，在基于矩阵乘积态表示的张量网络算法中，考虑了横向磁场中的量子伊辛模型和外磁场中的量子自旋1/2 Xyx模型.
英文摘要：
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding is based on the observation that, in the conventional Landau-Ginzburg-Wilson paradigm, a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking that is captured by a local order parameter, which in turn results in an essential change of the reduced density matrix in the symmetry-broken phase. Two quantum systems on an infinite lattice in one spatial dimension, i.e., quantum Ising model in a transverse magnetic field and quantum spin 1/2 XYX model in an external magnetic field, are considered in the context of the tensor network algorithm based on the matrix product state representation.
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